Step 1

Given: \(\displaystyle{n}={6}\)

probability of boy \(\displaystyle{p}={0.5}\)

probability of girl \(\displaystyle{q}={0.5}\)

The probability of getting exactly 5 boys is obtained using Binomial probability as below:

\(\displaystyle{P}{\left({X}={5}\right)}=_{{{6}}}{C}_{{{5}}}{\left({0.5}^{{{5}}}\right)}{\left({0.5}^{{{6}-{5}}}\right)}\)

\(\displaystyle={6}\times{0.03125}\times{0.5}\)

\(\displaystyle={0.09375}\)

Thus, the probability of getting Exactly 5 boys is 0.09375.

Step 2

Answer:

The probability of getting Exactly 5 boys is 0.09375.

Given: \(\displaystyle{n}={6}\)

probability of boy \(\displaystyle{p}={0.5}\)

probability of girl \(\displaystyle{q}={0.5}\)

The probability of getting exactly 5 boys is obtained using Binomial probability as below:

\(\displaystyle{P}{\left({X}={5}\right)}=_{{{6}}}{C}_{{{5}}}{\left({0.5}^{{{5}}}\right)}{\left({0.5}^{{{6}-{5}}}\right)}\)

\(\displaystyle={6}\times{0.03125}\times{0.5}\)

\(\displaystyle={0.09375}\)

Thus, the probability of getting Exactly 5 boys is 0.09375.

Step 2

Answer:

The probability of getting Exactly 5 boys is 0.09375.